Rodgers named an unchanged side from the midweek victory over Everton and Liverpool had an early chance to open the scoring after Yacob fouled Suarez and gave the Uruguayan the chance to replicate his recent successes from set-pieces with a free-kick but the resulting effort deflected out of play off the wall.
Suarez was picked out by his strike partner Sturridge but a resolute Baggies defence crowded Suarez and prevented any further danger in the attack. However in the 25th minute, Sterling broke down the wing and slipped the ball to Suarez who swept a cross to the back post which was cleverly met by Sturridge who opened the scoring with his 50th league goal.
West Brom could have been two down after 33 minutes when Suarez tried to convert from Coutinho's corner and Toure attempted to force the ball over the line but was thwarted by Foster and the defence as Liverpool had the momentum. Coutinho hit wide and at the other end, Gera hit a powerful effort that luckily for Mignolet sailed wide of the post.
The second half began with West Brom looking to level the score early and had a great chance after Gerrard had tripped Gera but Brunt curled the resulting free kick too high but had another good chance within minutes as he connected with a volley which was blocked by Flanagan.
Mignolet was forced into a superb save after a West Brom corner met the head of McAuley who tested the Belgian's reflexes but to no avail as Liverpool remained 1-0 in front but their lead could have increased just before the hour mark as Suarez swayed through the defence and was left with only Foster to beat but the finish was too close and the Englishman denied him.
West Brom drew level but in unbelievable circumstances as while in possession on the edge of his own area, Toure passed across the box and it rolled straight to Anichebe who finished superbly past Mignolet to the joy of the home fans while the travelling kopites could not believe what had just transpired.
Rodgers made an instant double swap as Allen and Kelly replaced Coutinho and Flanagan and Toure had a chance to make up for his error as a corner came into his path but he mistimed the header and it went wide.
Both sides pushed for a winner but had to settle for a point each but I think it is more a point gained for the hosts and two valuable points dropped for Liverpool in the fight for fourth place.